Find the domain and range of each function. See Example.ExampleEXAMPLE Find the domain and...

Find the domain and range of each function. See Example.

Example

EXAMPLE Find the domain and range of each function:

a. f(x) = 3x + 1

b.

Strategy For the domain, we will ask, “What values of x are acceptable replacements for x in 3x + 1 and ·” For the range, we will determine the set of output values.

WHY These values of x form the domain of the function and the set of output values is the range.

Solution

a. We will be able to evaluate 3x + 1 for any real-number input x. So the domain of the function is the set of real numbers. Since the output ycan be any real number, the range is the set of real numbers.

b. To find the domain of , we exclude any real-number x inputs for which we would be unable to compute The number 2 cannot be substituted for x, because that would make the denominator equal to zero. Since any real number except 2 can be substituted for x in the equation , the domain is the set of all real numbers except 2. Since a fraction with a numerator of 1 cannot be 0, the range is the set of all real numbers except 0.

{(0, 2), (1, 2), (3, 4)}